Problem: Given $ m \angle ABC = 5x + 12$, and $ m \angle CBD = 5x + 18$, find $m\angle ABC$. $B$ $A$ $D$ $C$
Answer: From the diagram, we see that together ${\angle ABC}$ and ${\angle CBD}$ form ${\angle ABD}$ , so $ {m\angle ABC} + {m\angle CBD} = {m\angle ABD}$ Since $\angle ABD$ is a straight angle, we know ${m\angle ABD = 180}$ Substitute in the expressions that were given for each measure: $ {5x + 12} + {5x + 18} = {180}$ Combine like terms: $ 10x + 30 = 180$ Subtract $30$ from both sides: $ 10x = 150$ Divide both sides by $10$ to find $x$ $ x = 15$ Substitute $15$ for $x$ in the expression that was given for $m\angle ABC$ $ m\angle ABC = 5({15}) + 12$ Simplify: $ {m\angle ABC = 75 + 12}$ So ${m\angle ABC = 87}$.